In a system for transmitting a digital signal using a direct sequence spread spectrum, the “0” and “1” bits are encoded with respective symbols sent by the transmitter, and decoded at the receiver by a finite impulse response (FIR) filter.
In the case where the bits are encoded using a spreading code of length N, the symbols encoding the “0” and “1” bits are each in the form of a series of N symbol elements distributed over either of two different levels and transmitted at a predetermined fixed frequency F.
The N symbol elements encoding the “1” bit are anti-correlated to the corresponding N symbol elements encoding the “0” bit, i.e., the symbol elements of the same rank within both of these two symbols have opposite values.
For example, if and when a symbol element of the symbol encoding the “1” bit is at level 1, the corresponding symbol element of the symbol encoding the “0” bit is at level −1. In the same way, if and when a symbol element of the symbol encoding the “1” bit is at level −1, the corresponding symbol element of the symbol encoding the “0” bit is at level 1.
The development of digital radio frequency (RF) communications, together with the expansion of mobile telephony, in particular, may demand the use of multi-standard, very low consumption RF receiver chains. To reach these objectives, an attempt is made to reduce to a minimum the difficult-to-program, analog RF circuitry, by bringing the analog-to-digital converter (ADC) as close as possible to the receiving antenna. This is then referred to as a digital/digital/digital receiver chain.
However, a solution such as this may have the effect of increasing the operating frequency of the ADC in an unreasonable manner. As a matter of fact, given the frequency of the signals involved in radio frequency communications, and taking into account the Shannon-Nyquist Theorem (sampling frequency equal to at least twice the maximum frequency of the signal being sampled), an operation such as this may necessitate the use of an ADC whose operating frequency would be on the order of several gigahertz. Such an ADC is currently commercially unavailable.
For this reason, it is conventionally impractical to process the signal digitally from the moment of reception. Nevertheless, this problem may be solved by undersampling the digital input signal. This technique, known by the name of undersampling, is based on the principal of spectrum overlapping and comprises sampling the signal received, not on the basis of Shannon's Theorem, but at a frequency greater than twice the signal bandwidth. This is typically valid only if the signal in question is a narrowband signal, i.e., if the bandwidth to carrier frequency ratio is significantly lower than one. Such being the case, the signals involved in the context of RF communications may be considered as such. As a matter of fact, their carrier frequency is typically on the order of 2.45 GHz for a bandwidth of a few MHz. Within this context of narrowband signals, it becomes possible, according to the undersampling theory, to sample the signals at a rate much lower than that suggested by the Shannon Theorem and, more precisely as explained above, at a sampling frequency that depends only on the bandwidth.
In order to illustrate the foregoing, FIG. 1 is a schematic representation of a signal receiving and processing chain, wherein the signal is captured by an antenna 10, then amplified by a circuit 20 referred to as LNA (for “Low Noise Amplifier”) prior to being submitted to the digital signal processing unit 30, referred to as DSP (for “Digital Signal Processing”). The output of the DSP unit may be processed conventionally by a processing unit 40, referred to as a CPU (for “Central Processing Unit”).
FIG. 2 is a schematic representation of the various functional units involved in the conventional digital solution of the DSP unit of FIG. 1, which implements undersampling.
The DSP unit includes an analog-to-digital converter 31. The signal being a narrowband signal, the sampling frequency Fe is not selected according to the Shannon-Nyquist Theorem, but according to the undersampling theory. Therefore, Fe is determined irrespectively of the modulation carrier frequency. In fact, it is assumed to be equal to at least twice the bandwidth of the binary message after spread spectrum. For example, for a bandwidth of 2B, the sampling frequency Fe≧4B. Furthermore, the analog-to-digital converter carries out an M-bit encoding, e.g., 4-bit.
The ADC is followed by a stage 32 for estimating the new carrier frequency fp, designating the new center frequency of the signal after undersampling, and by the phase φ corresponding to the carrier phase. The estimation stage will likewise make it possible to determine the minimum number of samples necessary for describing a bit time (Tb), i.e., the time to transmit one bit of the spread message, which depends, in particular, on the length of the spreading code used.
According to the undersampling theory, the carrier frequency of the signal is modified and assumes the following as a new value:
  fp  =      fm    -          k      ⁢              Fe        2            
where fm represents the initial carrier frequency and where k designates a parameter of the undersampling verifying:
  k  <            fm      -      B              2      ⁢      B      
The phase signal after undersampling is estimated by using a phase estimator.
The signal present at the output of the estimation stage will be filtered by a band-pass type filter 33, so as to retain only the base motif of the undersampled signal. As a matter of fact, since the spectrum of the undersampled signal consists of a multiplicity of spectral motifs representative of the message, a bandpass filtering operation is carried out in order to retain only a single spectral motif. Therefore, the characteristics of this bandpass filter are as follows:
Center frequency: fp
Bandwidth: 4B
The filter may be either an infinite or finite impulse response filter (IIR, FIR).
The signal is subsequently brought back to baseband by demodulation means 34. The undersampled message being conveyed to the carrier frequency fp, this demodulation step comprises a simple multiplication step using a frequency fp of phase φ sinusoid, these two characteristic quantities coming from the estimation stage.
A low pass filtering stage 35 at the output of the demodulation stage makes it possible to eliminate the harmonic distortion due to spectral redundancy during demodulation of the signal. As a matter of fact, the demodulation operation reveals the spectral motif of the baseband signal but also at twice the demodulation frequency, i.e., at about the frequency 2fp.
A matched filter stage 36 corresponding to the code of the wanted signal makes it possible to recover the synchronization of the signal being decoded with respect to the wanted information. More precisely, this is a finite impulse response filter, characterized by its impulse response coefficients {ai}i-0, 1, . . . , n.
Its structure, described in FIG. 3, is that of a shift register REG receiving each sample of the input signal IN. The shift register includes N bistable circuits in the case of symbols with N symbol elements, which cooperate with a combinational circuit COMB, designed in a manner known by those skilled in the art and involving the series of coefficients ai such that the output signal OUT produced by the filter has an amplitude directly dependent upon the level of correlation observed between the sequence of the N last samples captured by this filter and the series of the N symbol elements of one of the two symbols, e.g., the series of the N elements of the symbol encoding a “1” bit of the digital signal.
Thus, the matched filtering operation comprises matching the series of coefficients ai to the exact replica of the selected spreading code, in order to correlate the levels of the symbol elements that it receives in succession at its input to the levels of the successive symbol elements of one of the two symbols encoding the “0” and “1” bits, e.g., the symbol elements of the symbol encoding the “1” bit.
The output signal from the finite impulse response filter 36 can then be delivered to a comparator capable of comparing the amplitude of this output signal to a lower threshold value and to an upper threshold value, in order to generate a piece of binary information. The comparator is thus equipped to deliver, as a digital output signal representative of a decoded symbol of the input signal, a first bit, e.g., “1”, when the amplitude of the output signal of the filter 36 is higher than the value, and a second bit, e.g., “0”, when the amplitude of the output signal of the additional filter is lower than the lower threshold value.
However, the undersampling technique, which is suitable in this context, and upon which the digital processing of the signal from the moment of its reception relies, results in a degradation of the signal-to-noise ratio after processing, primarily when an interfering signal (typically the noise of the transmission channel) cannot be considered a narrowband signal. The conventional digital receiver chain as just described may have serious malfunctions once the noise power in the transmission channel becomes elevated.
As a matter of fact, as a result of the undersampling, the so-called spectrum overlap phenomenon may conventionally be observed wherein all of the frequencies higher than half the sampling frequency are “folded” over the baseband, causing an unacceptable increase in the noise power in the signal being processed. This results in an unacceptable error rate at the output of the decoding process.
This signal-to-noise degradation phenomenon in the transmission channel, amplified by the undersampling technique employed, is a principal reason for which the reception solutions based on digital/digital/digital receiver chains are at present dismissed, despite the undeniable advantages that they might obtain in terms of programming and consumption, in particular.
In order to attempt to improve this signal-to-noise ratio degraded after processing, various solutions may be anticipated, short of being satisfactory. In particular, it might be anticipated to increase the power of the signal upon transmission, which, however, involves a consequential increase in the electrical power consumed by the circuit. It might also be anticipated to use larger spectrum-spreading codes, but this would be detrimental to the speed, which would thereby be greatly reduced.